Damage Calculation

[Guvnor]

Look a little on the low side tbh

I made a boo boo in my calculation above. The sniping % goes in as an attack modifier according to this from the OP:

@SolemnWolf

Special Skills

Attacker: Zeline (Att=724x154%=1108, the capture dates from before the reduction of Zeline’s special skill)
Defender 1: Richard (Def=783x120%=940, powerful attack)
Calculated damage: (100x(1108/940)^1.35)x2=250 - Damage found: 212
Defender 2: Elena (Def=578x120%=694)
Calculated damage:100x(1108/694)^1.35=188 - Damage found: 181
Defender 3: Kadilen (Def=734x120%=881)
Calculated damage: 100x(1108/881)^1.35=136 - Damage found: 144
Defender 4: Domitia (Def=682x120%=818)
Calculated damage: 100x(1108/818)^1.35=151 - Damage found: 163
Defender 5: Vivica (Def=699x120%=839)
Calculated damage: 100x(1108/839)^1.35=146 - Damage found: 154

[BigLordF]

So the formula becomes:

Damage = 100 x [ (Theta x Att stat x Snipe % x Att modifier) / (Def stat x Def modifier) ] ^1.35

Or for my simplified purpose (Theta = 1, Defense = 1000, and no other modifiers)

Damage = 100 x [ (Att stat x Snipe %) / 1000] ^1.35 or even simpler

Damage = [Att stat x Snipe %] ^1.35 / 112

It’s been a long time since college so my math skills aren’t what they used to be but this looks good to me.

Am I far off?

(Sorry for the extra homework)

[Guvnor]

@BigLordF

Damage = 100 x [ (Att stat x Snipe %) / 1000] 1.35 or even simpler

Follow this & you should get some numbers
I don’t think your additional simplification works but I haven’t actually mathed it so

[BigLordF]

It’s the same thing. 1 / 112 = (100) / (1000) ^1.35

Or you can write it as 0.0089 and multiply it to the result.

[Lomaxx]

Hello,

I checked also on my side, especially using raids and special attacks.
Overall, it seems that the damage formula is less complex but it seems to be one for each character.
The basic formula D (damage) = a x (total attack) / (total defense) + b works quite well. There is a small piece of variance (random or based on other factor) that I did not search for (too time consuming).

Based on few tryouts I just did, I had good predicted results and an error factor between 0.1% and 6.8% which in my opinion is solid enough to use the formula (or to post it here).

I found a and b values by writing down battles statistics (raids and only special attacks) and MS excel gave me the trend line.

The values I have :

• Caedmon : a=238, b=189
• Gormek : a=243, b=79
• Leonidas : a=323, b=77

Example 1 : Caedmon total attack 754 vs Grimm total defense 640
Predicted damage = 238 * 754 / 640 + 189 = 469.39, real damage was 471 (error 0.3%)

Example 2 : Gormek total attack 659 vs Balthazar total defense 324 (492 -168)
Predicted damage = 243 * 659 / 324 + 79 = 573.25, real damage was 573 (error 0%)

Note : I don’t know if a and b values depend on other parameters like hero evolution, talents, raid arena…

I share this cos I had less than 1% error on 5 out of 8 tryouts so I was pretty excited.

I don’t pretend at all it is THE formula but it provided me sufficient results to know how to adapt know my strategy.
From a programming perspective this formula looks quite odd though…

Cheers

[Balltaser]

Can you give more details about the heroes you used: their levels, their stats, special skill levels, emblems etc. Maybe we could find common patterns to identify a and b.

[sonicbuster]

Kage has an attack by 988 and 450%, i hit the GM with defense 883 and got hit damage 737 and on another shot it was 720. but then i tried to calculate the damage by the formula, i can’t get this values. if formula this - 100х(988х4.5/883)^1.35=886. 886 and 737/720 - is very big difference. Is this a bug in the formula, or am I wrong?

[Balltaser]

Remember, he specifies that defending heroes get 20% boost, so GM’s defense would be 883 x 1.2 = 1060.

There is also a random factor ranging from .606 to 1.649.

Question: how much health did GM have? Kage deals 450% if the target has more than 50% health remaining, doesn’t he? Otherwise, it’s only 255%, I think.

[sonicbuster]

how much health did GM have?

close to 100%

[sonicbuster]

Of course, I heard about these mythical + 20% to defense, but it turns out that the defense team also has a higher attack. then the attackers are half as weak?)

[Dralya]

Hello,

Is the formule in post 1 is still right ? Date of the post is 03/2018.
I’m trying to make sort of a French Wiki
(And i’m very interrested by all calculation things in the game)

[Guvnor]

Yup, still matches up

[Guvnor]

Defending team gets ~1.2 multipler for both attack & defence

To compensate for all the advantages that the Attacking Team has & for how stupid the AI is comparatively.

[Gryphonknight]

@KalamityKaspar

Have you considered the possibility of θ being bounded by golden ratios?

The biggest problem with defining θ, there is a high likelihood of an attack stat soft cap common to grindy MMOs. Unlike other MMOs, Empires does not tell us the damage range. So a soft cap might be complicating our data set.

(Has SG 100% nerfed color stacking? - #63 by Garanwyn)

([Research] Does Color Stacking have a soft cap? or Attack stat research)

(Damage Calculation - #199 by Gryphonknight)

[Will_Braveheart]

I believe it likely you’re on the true path here. Have you gotten any closer to a conclusion on this point?

18 mos. playing and reading this thread I have come to the inescapable and logical conclusion that “Does x % damage” and “gets plus x% attack” are fundamentally DIFFERENT things and are likely accounted for inherently different.

Example, “does X % damage” would be applied to a calculation that RESULTS in a “base damage”, modifying it by the stated amount. The logical operation would be 1) Calc a “base damage”; 2) Apply damage (skill) modifier to achieve a “Final Damage”.

Expressed another way, Kage skill will ALWAYS increase the total damage yield, whatever it is, by the applicable % 450/225.

BT skill will increase the attack stat in the damage formula, whatever it really is lol, but may not yield an actual increase in calculated damage because it’s itself only a “factor” in the entire math operation.

The inherent difference being that damage % skill acts on the “result” of the base damage calc to yield a final number.

Forget the “Math” for a minute folks but follow the logic Admittedly, it’s been 20 years since I’ve had to “Math” professionally, but I been using logic my entire life. Idk

[baga]

unless there is a cap on that Att/Def ratio, something really fishy is going on.
my red raid stack includes BT and Santa (and Marjana). I often fire Marjana first, and then if lucky and charged Santa by the end of the battle, fire Marjana with BT’s special and enemy under Santa’s sack.
that should be:
[(1+0.48)/(1-0.44)]^1.35=(1.48/0.56)^1.35=2.64^1.35=3.7.
without specials, she hits for 700-800, with specials she rarely reaches 1k damage, which is nothing compared to 3.7 increase. it is not even 2.64 before exponentiation.

[ratabboypda]

@SolemnWolf

otro lado, una vez que el ataque es superior a la defensa, el daño puede volar sin u

And the person I think is very complicated to explain the damage, I would like to know in the formula that you ask where it was that you acquired each data, especially the 1.35 where this number comes from or if it is something randomly put that helps the formula to fit .
Damage ≈ 100 x (θ x Att / Def) ^ 1.35 I would like a more explained breakdown of each bone part:
damage I understand that part
100 I understand it refers to 100% damage
0 why?
att / def why?
^?
1.35? where does this number come from

I must also say that despite the predictions, the main topic is not being taken, which is not one but several.

• how can you calculate the board and which chips will come out
• the mana of a hero was not taken into account
  How can we calculate damage to the enemy if in many cases we do not know the value of their defense?
  I would like to know a little more about this, thank you very much.
  I think it’s great that more people get involved in answering these questions that some of us have been unable to sleep for months, trying to figure out this amazing game.
  greetings from argentina
  Ratabboy red de alianzas

[gingerhuny]

I know, this thread is referenced a lot for damage calculation… Super useful to so many players indeed

Hope one finds following to be also useful -

@gingerhuny

To anyone, if it helps… here is a simple table for how much damage to expect, for given attack and defense…

Note -

1. It doesn’t include possible variation in damage, which ensures that the number is not same every time.
2. It doesn’t include critical chance either.
3. Damage is most certainly not linearly proportional to attack or defense.
   i.e. In other words, +50% attack +50% defense does not mean same damage as without any buffs.
   And similarly +42% attack and -34% defense does not mean same damage as +74% attack.
4. DISCLAIMER - I am not responsible, if this table is incorrect… (and once again, I am in no way associated with SG… and make no guarantee, that this table is accurate or useful).

[TheWitcher]

Yes, only taking tile into account

[Nervicii]

So was doing some calculations. And when it comes to emblems it seems that 18 defense just never mitigates enough damage to warrant 36 hp.

Am I going wrong somewhere?
Even a lianna shot on a -44% down MN
4x 18 def, shot deals 1092 dmg. MN keeps 369HP
4x 36 hp, shot deals 1224 dmg. MN keeps 381HP

thoughts?